In Year 1, the economy plunges into recession with nominal GDP growth falling to minus -1 per cent. The inflation rate is subdued at 2 per cent per annum. The outstanding public debt is equal to the value of the nominal GDP and the nominal interest rate is equal to 2 per cent (and this is the rate the government pays on all outstanding debt). The government's budget balance net of interest payments goes into deficit equivalent to 1 per cent of GDP and the debt ratio rises by 4 per cent. In Year 2, the government introduces a fiscal stimulus and pushes the primary budget deficit out to 3 per cent of GDP to head of a recession. In doing so it stimulates aggregate demand and nominal GDP growth rises to 4 per cent nominal GDP growth rate. The central bank holds the nominal interest rate constant and inflation is stable. In Year 3, there is no change in monetary policy, and the government expands fiscal policy by an additional 1 per cent of GDP. Inflation is stable and nominal GDP growth rises to 6 per cent. From this data, you can conclude that
Answer: The debt ratio rises in Years 2 and 3 but the size of the increase (in percentage points) diminishes in the third year.
The answer is Option (a).
This question requires you to understand the key parameters and relationships that determine the dynamics of the public debt ratio. An understanding of these relationships allows you to debunk statements that are made by those who think fiscal austerity will allow a government to reduce its public debt ratio or that fiscal stimulus will blow the public debt ratio out.
While Modern Monetary Theory (MMT) places no particular importance in the public debt to GDP ratio for a sovereign government, given that insolvency is not an issue, the fact remains that in the case of the Eurozone nations there is a funding issue and so debt ratios do matter.
Each Eurozone nation has to fund its spending because of the simple fact that it surrendered its currency sovereignty the day it agreed to use a foreign currency - the Euro.
It can either fund from taxation revenue or bond-issuance on a sustainable basis. The bond markets know that each nation (Germany included) carries solvency risk although the practical extent of that risk varies significantly across the member nations and that variation is largely reflected in the differential bond yields.
A primary budget balance is the difference between government spending (excluding interest rate servicing) and taxation revenue.
The following equation shows the change in the public debt ratio (Δ B/Y):
The symbol, Δ is the Greek for change.
In English, this says that the change in the debt ratio is the sum of two terms on the right-hand side: (a) the difference between the real interest rate (r) and the real GDP growth rate (g) times the initial debt ratio; and (b) the ratio of the primary deficit (G-T) to GDP.
The real interest rate is the difference between the nominal interest rate and the inflation rate. Real GDP is the nominal GDP deflated by the inflation rate. So the real GDP growth rate is equal to the Nominal GDP growth minus the inflation rate.
The formula can easily demonstrate that a nation running a primary deficit can reduce its public debt ratio over time.
Furthermore, depending on contributions from the external sector, a nation running a deficit will more likely create the conditions for a reduction in the public debt ratio than a nation that introduces an austerity plan aimed at running primary surpluses.
But if growth is not sufficient then the public debt ratio can rise.
Here is why that is the case. While a growing economy can absorb more debt and keep the debt ratio constant or falling an increasing real interest rate also means that interest payments on the outstanding stock of debt rise.
From the formula above, if the primary budget balance is zero, public debt increases at a rate r but the public debt ratio increases at r - g.
So do some arithmetic to ensure you understand this. Refer to the Table below which shows the calculations.
Start by assuming a public debt ratio at the start of the Year 1 of 100 per cent (so B/Y(-1) = 1) which means that outstanding public debt is equal to the value of the nominal GDP. In the public debate a public debt ratio of 100 per cent would be very large and invoke all sorts of claims about solvency and persistently negative growth (the Spreadsheet Experts!).
If we also assume that in the current year (Year 1) that the nominal interest rate is 2 per cent and the inflation rate is 2 per cent then the current real interest rate (r) is 0 per cent.
If the nominal GDP grows at -1 per cent and there is an inflation rate of 2 per cent then real GDP is growing (g) at minus 3 per cent.
Under these conditions, the primary budget surplus would have to be equal to 3 per cent of GDP to stabilise the debt ratio (check it for yourself).
In Year 1, the primary budget deficit is actually 1 per cent of GDP so we know by computation that the public debt ratio rises by 4 per cent.
The calculation (using the formula in the Table) is:
Change in B/Y = (0 - (-3))*1 + 1 = 4 per cent.
In Year 2, monetary policy is unchanged and inflation is stable so the real interest rate remains at zero per cent.
From the Table below, note that the public debt ratio at the beginning of the period has risen to 1.04 because of the 4 per cent rise from Year 1.
The primary budget balance (deficit) rises to 3 per cent of GDP and nominal GDP growth recovers quickly and rises to 4 per cent, which means real GDP growth (given the inflation rate) is equal to 2 per cent.
The corresponding calculation for the change in the public debt ratio in Year 2 is:
Change in B/Y = (0 - 2)*1.04 + 3 = 0.92 per cent.
That is, the public debt ratio rises but at a slower rate than in the last year. The real growth in the economy has been beneficial and if maintained would start to eat into the primary budget balance (via the rising tax revenues that would occur).
In Year 3, real interest rate is zero, nominal GDP growth rises to 6 per cent (real GDP growth is 4 per cent) on the back of a rising primary budget deficit of 4 per cent.
The sustained growth leads to a reduction in the public debt ratio of 0.001968 percentage points, and the ratio at the beginning of Year 4 would be 1.0472 (104.72 per cent).
In a few years, the growth would also start to reduce the primary budget deficit as tax revenue rose and government maintained stable tax rates and spending growth rates.
The best way to reduce the public debt ratio is to stop issuing debt but that would require a dismantling of the Eurozone - a thoroughly recommended option.
But irrespective of that nuance, governments should go for growth and use expansionary deficits as the growth engine and then all the financial ratios that people worry about will take care of themselves.